The PS5 absolutely will cater to 4k 60fps at minimum, 4k 120fps will be common on many titles and 8k 30fps is something you will see on a morsel of titles.
The whole point of the Pro is to push 4k screen production and 4k content, so when the PS5 launches in a few years, pretty much everybody will be ready to take advantage of it with their 4k screens. In the meantime, PS4 is offering many native 4k games, dynamic 4k, close to 4k resolutions and checkerboarding 1800p etc....The fact that they can do all of that with HDR is a really impressive foray into UHD for consoles and I think current 4k screen owners will be impressed by the detail and clarity of their games through these rendering methods.
Lets put this in perspective..... I've had my 1080p screen for close to a decade, I bought it for the PS3, but the PS3 was predominantly 720p games and below. My 1080p screen gets maximum use from my PS4 since the majority of titles are 1080p, only from 2013, and yes, it's always a bummer when I see a 900p title on there, but that's not the worse we still have consoles like the XB1 from 2013 where common resolutions are 720p and 900p.......
I look at the Pro and it's only an iteration of the PS4 but look at the difference, I will be able to play so many 4k native games on it and so many games at resolutions that will be close like 3680x2070, 3520x1980 etc... and of course 1800p checkerboarded with HDR...Even geometry rendered 4k will be a big boost in image clarity over the resolutions we're seeing now...
So if you have to compare my 1080p experience on consoles. Pro is already delivering 4k native (1080p from 2013 consoles) and 1800p (900p from 2013 consoles) and resolutions even higher than 1800p. That's a far cry from what happened with my 1080p screen when I first purchased it years ago, I didn't have such native or close to native games to enjoy on the system 8-9 years back then. I only started enjoying consistent 1080p or even 900p content on it just 3 years ago, but with the Pro, I will be doing much better than that on day one with a 4k screen. So I believe the incentive to buy a 4k screen for the Pro is even greater than it was to purchase a 1080p screen for the PS3, and that's saying something, because the PS4.Pro is not the PS5, it's only a stopgap to usher in UHD gaming and content.